Jaya bought a car worth Rs. 350000 four years ago. If the value of the car…
2024
Jaya bought a car worth Rs. 350000 four years ago. If the value of the car depreciates over time at a fixed rate of 10% per annum, then what will be the present worth of the car?
- A.
229635
- B.
250000
- C.
230000
- D.
266150
Show answer & explanation
Correct answer: A
When a value depreciates at a fixed rate every year on a REDUCING BALANCE, the amount remaining after n years is Final Value = P x (1 - r)n, where P is the original price and r is the annual depreciation rate written as a decimal. This is the same reducing-balance idea used in compound interest, except the multiplier (1 - r) is less than 1 because the value shrinks instead of growing.
Original price P = Rs. 350000, annual depreciation rate r = 10% = 0.1, so the year-on-year multiplier is (1 - 0.1) = 0.9.
After year 1: 350000 x 0.9 = 315000.
After year 2: 315000 x 0.9 = 283500.
After year 3: 283500 x 0.9 = 255150.
After year 4: 255150 x 0.9 = 229635 - this is the present worth of the car.
As a check, the same result follows directly from the reducing-balance formula: 350000 x (0.9)4 = 350000 x 0.6561 = 229635, confirming the step-by-step calculation.